The  Musical  Scale  of  the  Arabs. 

Medieval  Organ  Pipes  and  Their  Bearing 
On  the  History  of  the  Scale. 

The  Natural  Diatonic  Scale. 


CHARLES  K.  WEAD, 

U.  S.  Patent  Office,  Washington,  D.  C. 


EASTON,  PA.: 

THE  CHEMICAL  PUBLISHING  COMPANY 

1900. 


[From  the  Proceedings  of  the  American  Association  for  the  Advancement 
of  Science.  Vol.  48,  ifsgg.l 

The  Musicae  Scales  of  the  Arabs.  By  Charles  K.  Wead,  U.  S. 

Patent  Office,  Washington,  D.  C. 

The  views  of  the  Arab  scales  quoted  by  Helmholtz  and  others  from 
Kiesewetter  and  Villoteau  must  be  recognized  as  unsound,  now  that  Dr. 
Land  has  given  a translation  of  the  “ Book  of  Music”  of  A1  Farabi,  who 
died  950  A.  D.  This  proves  that  musicians  demanded  different  scales  for 
different  instruments,  although  those  for  the  short-necked  lute  were  the 
most  important.  This  lute  had  five  strings  tuned  in  fourths  ; for  the  lit- 
tle finger  of  the  left  hand  a ligature  (fret)  was  tied  around  the  neck  at  a 
quarter-length  of  the  string,  so  giving  a fourth  ; in  the  space  up  to  the 
nut  eight  other  ligatures  were  tied  according  to  various  rules  , some  by 
calculating  intervals  of  a tone  as  the  Greeks  did,  others  by  bisecting  the 
linear  distance  between  two  ligatures  : thus  arose  a scale  of  twenty-two 
steps  to  the  octave.  But  the  notes  due  to  the  bisections  fall  in  close  pairs; 
so  two  steps  in  each  tetrachord,  or  five  in  the  octave,  were  very  short ; ac- 
cordingly later  theorists  substituted  for  each  pair  a third  note  determined 
by  Greek  principles  and  thus  obtained  the  17-step  scale  that  has  provoked 
so  much  controversy.  Out  of  these  many-note  scales,  various  short  scales 
or  ” modes”  were  selected  for  musical  performance  ; these  modes  usually 
called  into  exercise  only  three  out  of  the  four  fingers,  and  so  had  eight 
notes  to  the  octave. 

On  the  long-necked  tambours  the  ligatures  were  located  by  almost  en- 
tirely different  principles,  the  most  important  being  a “step-by-step  tun- 
ing,” nowhere  else  described  in  musical  history  ; as  applied  on  the  two- 
stringed tambour  of  Bagdad,  this  principle  gave  within  a total  compass  of 
about  a minor  third  a scale  of  eight  notes. 


Medieval  Organ  Pipes  and  Their  Bearing  On  the  History  of 
THE  Scale.  By  Charles  K.  Wead,  U.  S.  Patent  Office,  Washing- 
ton, D.  C. 

The  question  of  the  origin  and  basis  of  the  scale  currently  accepted  by 
European  musicians  is  now  receiving  much  attention.  Some  vigorous 
writers  maintain  that  it  is  based  wholly  on  harmonic  considerations, 
which  apply  also  with  equal  force  to  all  peoples  who  have  not  been  led 
astray  by  instruments.  I feel  most  decidedly  that  this  conclusion  is  a 
hasty  generalization,  which  has  taken  account  only  of  a few  classes  of 
facts,  and  especially  has  ignored  the  history  of  the  development  of  the 
European  scale.  Both  as  a contribution  to  one  branch  of  this  history, 
and  as  a matter  having  independent  interest,  a brief  account  is  to  be  given 
of  the  history  of  organ-pipe  tuning  from  the  earliest  times  of  which  we 
have  knowledge  of  it  ; no  English  writer  refers  to  the  matter  at  all,  and 
the  few  Germans  who  quote  some  of  the  documents  of  importance  here 
do  not  consider  their  bearing  on  the  subject  of  the  scale. 


2 


PAPERS  READ. 


Not  much  is  known  of  the  organs  prior  to  the  tenth  century.  The 
broad  idea  of  blowing  a series  of  whistles  (fistulae)by  air  compressed  by 
a bellows  belongs,  as  is  familiarly  known,  to  classical  times,  and  in  our 
modern  histories  of  the  instrument  there  are  various  references  to  organs 
during  the  Dark  Ages,  as  one  sent  to  Pepin  (757  A.  D.),  and  one  to 
Charlemagne  a little  later,  which  last  is  said  to  have  been  the  first  organ 
used  in  a church  in  the  West ; but  by  the  close  of  the  eleventh  century 
instruments  were  in  use  in  several  places.  Rimbault  quotes  a bungling, 
sometimes  unintelligible,  translation  of  an  Xlth  century  MS.,  which 
gives  many  details  of  the  manufacture  of  pipes.  But  a far  more  important 
as  well  as  earlier  account  is  found  in  a MS.  of  the  Xth  century,  from  the 
German  translation  of  which  in  Wangemann’s  Geschichte  der  Orgel  we 
quote  at  length.  By  way  of  preface  it  should  be  noticed  that  all  musical 
theory  underlying  these  mechanical  rules  is  due  to  Boethius  (c.  525  A.  D. ), 
whose  somewhat  ignorant  Latin  compilation  from  Greek  musical  writers 
served  men  admirably  during  the  years  when  scholasticism  demanded,  not 
experimental  truth,  but  authority.  So  the  Greek  ideas  of  three  genera,  of 
tetrachords,  of  ditones  instead  of  our  major  thirds,  of  Pythagorean  ratios, 
of  divisions  of  the  monochord,  etc.,  are  everywhere  to  be  found  in  these 
medieval  writers.  At  the  same  time  there  is  a good  deal  of  variety  in 
their  practical  ways  of  teaching  the  subject,  and  we  shall  see  how  they 
gradually  emancipated  themselves  from  these  fettering  theories. 

This  Xth  century  MS.  gives  many  practical  details  about  the  manufac- 
ture of  organ  pipes.  They  were  to  be  made  of  thin  sheet  copper  rolled 
into  cylinders  about  four  feet  long,  all  having  the  diameter  of  a pigeon’s 
egg  (a  little  over  an  inch).  The  lengths  were  measured  from  the  mouth 
up.  “ And  now  since  it  is  the  diatonic  genus  in  which  at  present  for  the 
most  part  songs  move,  the  pipes  are  measured  as  follows  : The  first, 
which  is  smaller  and  therefore  higher  than  all  the  rest,  must  be  divided 
into  eight  parts,  and  by  an  eighth  part  of  the  first  must  the  second  be 
greater  than  the  first,  in  order  that  they  may  differ  by  a tone.  Just  so  the 
third  must  be  greater  than  the  second  by  an  eighth  part,  and  a tone  lie 
between  them.  Then  it  must  be  so  arranged  that  the  fourth  is  greater 
than  the  first  by  the  third  part  of  the  first,  so  that  it  differs  from  the  first 
by  a fourth,  and  from  the  third  by  a half-one.  And  the  fifth  must  be 
greater  than  the  first  by  a half  of  the  first,  so  that  it  forms  the  pure  fifth 
to  it,  but  a tone  with  the  fourth.  The  sixth  must  be  greater  than  the  fifth 
by  an  eighth  of  the  fifth,  and  have  a tone  between  them.  The  seventh 
must  be  greater  than  the  fourth  by  a third  part  of  the  fourth  in  order  to 
form  with  it  a fourth,  but  a half-tone  to  the  sixth.  The  eighth  has  the 
double  length  of  the  first,  and  is  distant  from  it  by  a pure  octave,  which 
is  always  made  up  of  a fourth  and  a fifth.  The  same  operation  as  in  the 
measurement  for  the  second  pipe  is  to  be  repeated  to  determine  the  series 
from  the  octave  up  in  the  order  that  we  have  given.  With  the  seven 
tones  of  the  octave  described  one  can  by  rising  and  falling  produce  every 
song.”  Then  follow  details  of  mechanism — several  pipes  in  unison  or 
octaves,  sometimes  as  many  as  five  or  ten,  might  be  arranged  to  each 


SECTION  B. 


3 


valve,  the  longer  pipes  being  at  the  player’s  right  hand.  Connected  to 
the  valves  by  iron  wires  were  certain  wooden  plates  (keys?)  bearing  the 
“ letters  of  the  alphabet  written  twice,  thus  : 

ABCDEFGABCDEFGH 
in  order  that  the  player  may  more  quickly  see  which  plate  he  should 
strike.” 

A second  rule  for  pipe  lengths  is  then  given,  as  if  this  anonymous  MS. 
was  a collection  from  various  sources  ; it  was  thus  : “He  who  would 
know  the  measures  and  construction  of  an  organ  must  first  of  all  imagine 
eight  pipes  having  the  same  length  and  thickness,  but  all  larger  above 
than  below  (i.  e.,  conical).  Then  take  the  first,  which  may  be  long  or 
short,  at  pleasure  ; to  find  the  relation  of  the  second  to  it  divide  the  first 
into  nine  parts  and  make  the  second  equal  to  8 : 9 of  the  first  ; similarly 
divide  the  second  pipe  into  nine  parts,  and  give  the  third  again  8 ; 9 of 
the  second;  to  get  the  correct  measure  of  the  fourth  pipe  give  it  3 : 4 of  the 
first.  The  fourth  pipe  divide  into  nine  parts,  and  the  fifth  must  be  in 
length  8 : 9 of  it,  as  well  as  the  sixth  8 : 9 of  the  fifth.  The  seventh  again 
is  3 : 4 of  the  fourth,  while  the  eighth  is  8 ; 9 of  the  seventh.  When  these 
eight  are  ready  one  goes,  in  the  same  way  as  from  the  first  to  the  eighth, 
from  the  eighth  to  the  fifteenth,  the  octave  of  the  eighth,  and  from  the 
fifteenth  to  the  twenty-second,  the  octave  of  the  fifteenth.”  To  each 
valve  there  are  to  be  arranged  two  longer  pipes  and  a shorter  one  placed 
between  them  ” that  the  three  pipes  may  give  a consonance,  the  so-called 
octave  apparently  the  compass  was  as  before  only  two  octaves. 
Wangemann  seems  to  overlook  the  fact  that  these  two  rules  give  totally 
different  successions,  for  the  first  is  a descending  scale — increasing  pipe 
lengths  ; the  second  an  ascending  scale.  The  first  nominally  gives  a 
series  of  intervals  approximately  the  same  as  from  our  a down  to  A,  while 


the  second  gives  approximately  G to  g,  thus  : 

G 

A 

B C 

D 

E 

F 

G a 

First  Rule  | T 

2 

I 

1 n 

3 

T 

4 

3_ 

f 

8 1 
6f 
8 1 
12  8 

8 T 

¥ I 

T6  i 

Second  Rule  i 

8 

■9 

n f 

2 

3 

if 

i 

If  these  two  scales 

have 

any  note  in  common  they  agree 

throughout. 

for  each  number  in  the  last  line  is  8 : 9 of  the  number  directly  above  it. 

But  any  one  who  has  the  slightest  knowledge  of  organ-pipe  construction 
knows  that  all  these  intervals  would  in  practice  be  found  quite  flat,  the 
shorter  pipes  being  relatively  too  long,  and  even  the  octaves  sounding 
together  in  the  way  just  described  would  be  very  unsatisfactory.  So  it  is 
interesting  to  see  how  early  the  inadequacy  of  these  rules  was  recognized. 

A MS.  of  the  Xth  century  attributed  by  Gerbert  to  Hucbald  gives  the 
following  rule,  which  Wangemann,  who  quotes  it  along  with  those  just 
given,  strangely  says,  offers  nothing  new  : ‘‘If  the  pipes  are  of  equal 
diameter  and  the  greater  contains  the  less  twice  in  its  length  and  in  addition 
its  diameter  they  will  mutually  sound  the  consonance  diapason  [octave]. 
* * If  the  greater  pipe  contains  the  less  a whole  time  and  a third  part 


4 


PAPERS  READ. 


of  its  length  besides,  and  also  a third  part  of  the  diameter  of  the  hollow 
[i.  e.,  of  the  internal  diameter],  they  will  sound  a diatessaron  [fourth].” 
Other  ratios  given  are,  for  the  double  diapason  four  times  the  length  of 
the  shorter  pipe  plus  three  diameters ; for  the  diapenute,  or  fifth,  one 
and  a half  lengths  and  half  the  diameter ; for  a tone,  one  length  and  an 
eighth  ; and  for  a semitone,  one  length  and  a sixteenth.  These  rules 
give  intervals,  but  not  directly  a scale  in  which  the  semitones  are  definitely 
located. 

But  Hucbald  has  several  other  rules,  one  of  which  gives  the  succession 
nominally  as  from  C to  c,  thus  : 

, 8 64  3 2 16  128  1* 

I 9 8T  4 3 -21  243  2 

In  one  passage  he  says  the  first  (highest)  pipe  should  have  a length 
eight  times  its  diameter. 

Odo  in  the  same  century  gives  clearly  a different  idea  of  getting  out  his 
ratios,  though  the  results  are  the  same,  and  he  brings  in  both  b and  b 
flat.  He  says  : “In  the  measures  of  pipes  there  ate  the  notes 
C D E F G a t;  c . 

“ The  length  of  low  C is  to  be  taken  at  pleasure  ; this  is  divided  into  four 
parts  and  one  part  being  subtracted  leaves  the  pipe  F.’’  His  further 
details  may  be  condensed  to  a line  thus  : 

G-:=|  C;  D---I  G;  a=|  D;  E-f  a;  Q[=b]=.f  E;  b[=b^]=f  F. 

“ Further,  the  skilful  musician  observes  that  these  measures  are  estab- 
lished by  fourths  and  fifths,”  quite  in  the  spirit  of  nineteenth  century 
tuners,  only  he  worked  by  measure,  they  by  ear. 

By  far  the  fullest  account  of  rules  for  pipe-lengths  is  given  in  the 
tractate  De  Musica  by  one  of  the  brothers  of  St.  Gall,  written  in  Old 
High  German  in  the  same  tenth  century.  The  MS.  Gerbert  used  was 
very  imperfect,  and  Riemann  has  corrected  his  readings  by  the  aid  of  the 
fine  Leipzig  Codex.  Not  the  least  important  point  is  the  frequent 
implication  that  the  instruments  were  to  guide  the  voice  ; so  rules  are 
first  given  for  the  lyre  and  psaltery  ; but  it  is  said  to  be  difficult  to  get 
the  length  of  strings  right,  for  if  too  long  they  are  scarcely  sonorous  and 
the  tone  is  poor,  while  if  too  short  the  higher  tones  are  thin.  But  he  who 
measures  off  organ  pipes  avoids  these  difficulties.  “ It  is  said  that  a pipe 
for  the  first  letter  [A]  one  ell  in  length  from  its  lip  up  is  too  short,  and 
one  of  two  ells  is  too  long  ; but  those  between  the  two  having  a length  of 
an  ell  and  a half  are  suitable.”  The  only  figures  I find  for  the  ell  of 
St.  Gall  (unfortunately  of  much  later  date)  give  it  as  almost  exactly  24 
English  inches  ; so  this  lowest  pipe  would  have  been  about  36  inches  long, 
and  have  given  a note  between  d and  f (on  the  bass  staff)  of  our  modern 
pianos.  The  uncertainty  is  because  we  do  not  know  the  diameter  of  the 
pipe  which  was  to  be  “ so  wide  as  pleases  you.”  The  rules,  which  are 
so  long  that  it  might  be  tedious  to  quote  them,  give  an  ascending  scale, 
with  both  minor  seventh  (called  synemenon)  and  major,  all  corrected  for 
influence  of  diameter  nearly  in  the  same  way  as  stated  by  Hucbald  ; thus 


SECTION  B. 


5 


“ take  from  the  length  of  the  first  pipe  the  eighth  part  of  its  width  and 
divide  it  from  the  point  down  to  the  lip  * * * into  nine  parts  of 

equal  size  ; give  eight  of  these  to  the  second  pipe  ; this  is  its  length  from 
the  tip  up.  ’ ’ 

The  same  Leipzig  Codex  contains  a curious  rule  that  makes  the  ratio  for 
a tone  7 : 8 instead  of  8 ; 9.  The  author  starts  from  A and  ascends  in  pitch, 
so  obtaining  results  that  may  be  tabulated  as  follows : 


His  notation A 


Modern  notation  A 
Or C 


I 


B . C D 

B C # D 

D . E F 


1 

8 


E . F . G a 

E F # G # a 

G . A . B C 

H • m . mi  I 


Riemann  treats  this  ratio  7 : 8 as  the  rough  equivalent  of  Notker’s  ratio 
8 : 9 together  with  this  correction  for  diameter  ; but  this  is  inadmissible, 
for  the  fourth  and  octave  are  not  corrected  and  so  the  two  semitones  are 
almost  vanishingly  small,  or  rather  what  should  be  the  lower  note,  comes 
out  the  higher  one  ! 

Aribo,  in  the  next  century,  gives  Notker’s  rules,  and  others  due  to 
Monk  Wilhelm  with  corrections  based  on  different  fractions  of  the 
diameter.  And  many  more  rules  might  be  quoted. 

Coming  to  more  recent  times,  there  is  a little  to  be  found  in  Father 
Kircher’s  voluminous  Musurgia  Universalis,  published  in  1650.  He  says 
the  ratio  of  circumference  to  length  of  organ  pipes  varies  very  much,  as 
from  one-fourth  to  three-fifths ; two-fifths  was  perhaps  most  usual 
( giving  a diameter  one-eighth  of  the  length  as  stated  by  earlier  writers ) . 
His  lengths  follow  the  familiar  modern  ratios,  i : 2,  2 ; 3,  3 : 4,  4 ; 5,  8 ; 9. 
He  does  not  refer  to  any  correction  for  diameter,  which  would  be  of 
large  importance  with  such  large  pipes,  nor  does  he  speak  of  tuning  the 
pipes  after  they  are  made.  A century  more  shows  a marked  advance  ; 
for  in  the  great  book  of  Bedos  de  Celles,  “ L’art  du  Facteurs  d’Orgues,” 
Paris,  1766,  while  rules  are  given  for  fixing  the  pipe-lengths,  proceeding 
by  fourths  and  fifths,  there  are  also  directions  for  tuning  by  cutting  the 
pipes  off  afterward  to  the  exact  desired  pitch,  and  in  the  plates  there  are 
figures  of  tuning-cornets  such  as  are  used  to-day.  Lastly,  in  the  great 
Encyclopedie  (1750),  under  “ Diapason,”  it  was  directed  that  to  the 
computed  length  as  given  by  such  rules  as  the  above  some  inches  shall 
be  added  to  allow  for  contingencies  of  tuning. 

These  citations  are  enough  to  show  how  slowly  our  ancestors,  starting 
from  the  purely  mechanical-mathematical  scale  inherited  from  the  Greeks, 
and  practically  fitted  only  for  a thin-stringed  monochord,  progressed  to 
the  series  of  notes  of  to-day,  that  is  independent  of  any  particular 
instrument.  Historically,  development  of  the  scale  has  gone  along  with 
the  development  and  perfection  of  instruments,  first  of  the  organ  and  then 
of  the  piano.  In  the  organ  the  wind  supply  needed  great  improvements 
before  a steady  tone  could  be  produced,  and  it  was  not  till  the  invention 
of  the  wind-gauge  in  1677  that  this  was  fairly  accomplished.  Meantime 
other  improvements  had  been  going  on  ; the  keys  were  narrowed,  the 


6 


PAPERS  READ. 


many  pipes  to  a single  key  were  distributed  to  registers,  and  pedals  and 
black  keys  had  been  introduced.  But  all  the  time  that  the  ideas  of  poly- 
phony and  incipient  harmony  were  growing,  the  king  of  instruments  was 
not  fitted  to  furnish  a single  interval  that  would  be  at  all  acceptable 
to-day.  In  fact  Praetorius,  who  died  in  1621,  thirty  years  after  Palestrina’s 
death  and  seventy-five  years  after  Luther’s  death,  says  one  reason  for  the 
slow  development  of  harmony  was  that  ‘ ‘ the  tones  and  semitones  were 
not  turned  correctly,  and  therefore  the  instruments  or  organs  were  not 
turned  so  ‘justly’  as  at  present.”  The  errors  of  the  old  rule  were  very 
great ; two  pipes  of  36  and  18  inches  length  above  the  lip  and  2^  inches 
diameter,  according  to  Kircher’s  proportion,  would  not  be  an  octave  apart, 
but  only  a little  over  ten  semitones,  as  C-A  ; perhaps  the  early  pipes  were 
slimmer  and  the  error  less,  so  the  corrected  rule  might  give  a fair  approx- 
imation to  correct  intervals  ; still  the  correction  is  not  more  than  half  or 
three  fifths  of  that  required  by  the  rules  of  the  famous  modern  French 
organ  builder,  Cavaille-Coll. 

There  is  one  more  stage  in  the  history  of  our  scale.  After  the  organ  had 
been  so  far  perfected  that  any  desired  intonation  (^.  ^.,  just,  mean-tone 
or  equal  temperament)  could  be  given  to  it,  keyed-stringed  instruments 
were  developed  with  not  a little  deliberate  imitation  of  organ  ideals,  as 
those  know  who  saw  the  Steinert  collection  at  the  Chicago  Exposition. 
As  the  logical  outcome  of  the  demand  on  the  part  of  the  growing  harmony 
for  freer  modulation  into  all  keys  there  was  a modification  of  the  old 
Pythagorean  and  harmonic  tunings,  as  well  as  of  the  mean-tone  tempera- 
ment, finally  resulting  in  the  equal  temperament.  This  could  be  carried 
out  conveniently  on  the  stringed  instruments  ; it  was  more  needed  for  the 
kind  of  music  written  for  them,  and  the  short  duration  of  their  sounds 
rendered  the  deviations  of  the  tuning  from  perfect  concords  less  offensive 
to  the  ear  than  when  it  was  practiced  on  the  long-drawn  notes  of  the 
organ.  But  musicians  found  it  unsatisfactory  to  try  to  maintain  several 
standard  scales,  so  the  clavichord  and  piano  have  in  spite  of  bitter  oppo- 
sition, forced  their  peculiar  scale  upon  the  European  musical  world,  till 
orchestra,  voices,  and  finally  the  organ  have,  with  practical  unanimity, 
surrendered  to  it.  Of  course  this  is  a ‘‘survival  of  the  fittest,”  but  the 
statement  only  means  the  fittest  for  a particular  environment  ; for  other 
environments  it  would  not  necessarily  be  the  fittest ; e.  that  of  an 
Oriental  or  savage  musician,  of  a .string  quartette  or  of  Europeans  a cen- 
tury hence. 

Finally  it  is  to  be  observed  that  instruments  have  been  the  guides  to  the 
voice  in  all  these  ages  under  consideration.  Guido,  who  died  in  1050, 
taught  his  boys  the  intervals  by  the  aid  of  the  monochord,  which  he  im- 
proved for  this  purpose.  In  later  times  the  organs  served  a similar 
purpose,  as  appears  from  the  remark  of  Praetorius,  who  says  : ‘‘That  the 
compass  remained  narrow  for  so  long  a time  is  because  the  organ  was  used 
onlj  to  accompany  choral  singing,  and  no  great  range  was  required,  for 
harmony  was  unknown,”  and  he  distinctly  says  that  only  the  bare  choral 
in  one  part  was  performed  on  them.  Even  to-day  what  pupil  learns  to  sing 


SECTION  B. 


7 


intervals  correctly  except  by  directly  or  indirectly  imitating  an  instru- 
ment ? As  instruments  have  developed,  both  the  scales  embodied  in  them 
and  the  ideas  of  musicians  concerning  the  scale  have  changed,  responding 
to  distinctly  traceable  influences  ; and  there  is  no  hint  in  the  long  history 
that  the  “ harmonic  consciousness,”  on  which  to-day  much  stress  is  laid 
by  some  writers,  has  ever  failed  to  content  itself  with  the  scale  familiar  to 
it,  however  wide  the  departures  from  a true  harmonic  scale.  So  if  in  the 
fields  where  harmony  has  won  practically  all  its  triumphs  there  is  no 
proof  of  a scale-making  “harmonic  consciousness,”  may  we  not  ask  for 
substantial  evidence  that  it  exists  among  peoples  who  have  no  harmony  ? 
And  may  we  not  expect  that  ample  explanation  of  the  facts  alleged  in 
support  of  this  view  will  be  found  when  all  the  circumstances  of  the  in- 
vestigation are  made  known  ? 

This  brief  presentation  of  one  phase  of  musical  history  should  convince 
the  student  that  the  opposing  views  regarding  the  basis  of  the  scale  so 
dogmatically  presented  by  extreme  physicists  or  extreme  musicians  are 
alike  inadequate,  because  they  disregard  r.hy  historical  elements  of  the 
problem. 

Note. — The  historical  authorities  for  the  principal  statements  made 
above  are  as  follows  : Rimbault,  E.  F. : The  History  of  the  Organ,  Lon- 
don, 1870:  Wangemann,  O.:  Geschichte  der  Orgel,  Demmin,  1880,  p. 
66,  69,  70,  91.  Gerbert,  M.  : Scriptores  ecclesiastici  de  musica  sacra,  1784, 
as  reprinted  in  Migne’s  Patrologia  Latina,  Vols.  131,  132,  133,  under  the 
names  of  Hucbald,  Odo,  Notker,  and  Aribo.  Reimann,  H. : Studien  zur 
Geschichte  der  Notenschrift,  Leipzig,  1878,  p.  298.  The  argument  for  the 
“harmonic  consciousness”  is  strongly  put  by  the  late  Professor  J.  C. 
Fillmore  in  Omaha  Indian  Music,  Cambridge,  1893. 


The  Naturae  Diatonic  Scaee.  By  Charees  K.  Wead. 

This  paper  gives  an  account  of  the  history  of  the  three  words  in  the 
title.  In  the  mediaeval  tables  those  hexachords  involving  the  use  of 
b-molle  (b  b)  were  called  mo  lie  ; those  involving  b-dur  (b  natural)  were 
called  dur  ; and  those  that  did  not  involve  either  b,  but  applied  Guido’s 
six  syllables  to  the  letters  in  their  natural  order  from  A up,  were  called 
natural  hexachords  ; the  other  things  and  names  have  lost  interest  for 
modern  musicians,  and  the  so-called  “ natural  ” series  remains,  and  re- 
tains the  name.  ” Diatonic”  refers  generically  to  those  tunings  of  the 
intermediate  strings  of  the  Greek  lyre,  located  between  E and  A,  in 
which  the  strings  were  most  “ on  the  stretch,”  and  so  gave  their  highest 
tones,  and  specifically  to  the  highest  of  these  tunings,  the  one  giving 
substantially  the  same  succession  as  our  E,  F,  G,  A.  “ Scale  ” is  not 
found  in  use  till  after  1500  ; the  old  word  for  the  series  of  sounds  was 
sy sterna  ; for  the  notes  on  paper,  diagram.  Scala  at  first  referred  to  the 
tables  of  hexachords,  then  to  notes  arranged  on  lines  and  in  spaces,  and 
finallv  to  the  series  of  sounds,  which  is  now  the  exclusive  meaning. 


Digitized  by  the  Internet  Archive 
in  2016 


https://archive.org/details/musicalscaleofarOOwead 


BOSTON  COLLEGE 


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